Machine Learning Optimization of a Low Pressure Steam Turbine Stage

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Large language models have made AI/ML front-page news, but, as with so many computational technologies, the CFD industry has been breaking ground in this field for a long time, and Cadence Fidelity CFD software was one of those groundbreakers. But unlike processing a JPEG or snippet of text grabbed from the internet, a CFD computation can take many hours, so we need our machine learning algorithms to deliver results with as few inputs as possible - we're talking about a model with dozens, not billions, of parameters. All that said, an automated, AI/ML-accelerated process for finding an optimal design is still orders of magnitude faster than tweaking everything by hand.

Automated design optimization replaces the laborious process of making small modifications to CAD models and flow conditions by hand in order to seek better designs. Like many other technologies, it does not replace the engineer but frees up the engineer to pursue other tasks. In this case, the focus and energy of the design engineer is shifted away from setting up and running simulations to understanding and analyzing design spaces. Because CFD computations are so time-consuming, development of efficient methods of design space exploration methods that find the optimum quickly has been critical to make automated design optimization a viable technology for the design of turbomachinery components. In this article, we will explore how the Fidelity Fine Turbo and Fidelity Fine Design3D products have been used to optimize a low-pressure (LP) steam turbine stage.

The goal of this optimization project is to retrofit this stage with a new design that will increase the system’s power. Since the scenario is that we are retrofitting an old machine with new power, the geometry of the original machine imposes fundamental constraints and requirements that must be respected in the new design. Thus, the stator cavity, bearing, and nozzle vanes are fixed, while the wheel vanes and rotor tip leakage cavity are targets for optimization.

Overview of the Design Space

Cadence’s Fidelity software suite includes a design tool in partnership with Concepts NREC, Fine Agile, which is a design, analysis, and geometry generation tool for turbomachinery. Using Fine Agile, we can parameterize the design space appropriately and impose constraints. Table 1 shows how the tip leakage cavity is parameterized, while Table 2 shows the values for the blade shape. In total, eight parameters are adjusted during the optimization run.

	Cavity Design parameter	Allowed range
1	Top width of labyrinth seal tooth	2-5 mm
2	Labyrinth seal tooth asymmetry	0-1
3	Labyrinth seal tooth axial offset	±5 mm

Table 1: Cavity design space

	Cavity Design parameter	Allowed range
1	Top width of labyrinth seal tooth	2-5 mm
2	Labyrinth seal tooth asymmetry	0-1
3	Labyrinth seal tooth axial offset	±5 mm

Table 2: Blade design space

Fidelity Fine Design3D software is based on a sophisticated machine learning kernel that uses an evolutionary algorithm to drive a surrogate model based on an initial design of experiments (DoE) run to an optimum that stays within defined constraints. First, a DoE is run by doing full CFD simulations using the eight parameters provided, populating the design space with a few points. A surrogate model is defined as a response surface fit to these points. Fine Design3D then intelligently explores this space, varying the input parameters, running more simulations, updating the model, and iteratively refining until an optimum is found.

To generate the initial solutions, a CFD simulation is set up according to best practices. A low-Re mesh of 1.8m cells was generated for a single passage, and simulations were run using Fine Turbo. Water steam was used as the fluid, and the Spalart-Allmaras turbulence model was used to generate steady-state solutions. More detailed parameters of the simulation are given in Table 3.

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Figure 1: The initial simulation geometry

Turbulence model	Spalart-Allmaras
CFL	3
Fluid	Water steam (thermodynamic tables)
Initial solution	For turbomachinery + techno effects
Inlet	Total pressure and enthalpy imposed, flow is normal to the inlet
Walls	Rotor - Rotation speed and adiabatic (3000rpm) Stator - Static and adiabatic
Outlet	Static pressure (radial equilibrium)
Time configuration	Steady
R/S	Full non-matching mixing plane
Output quantities	Power, Axial thrust, mass flow, (convergence)

Table 3: Simulation parameters

The design space for the LP turbine stage has 12 dimensions. There are the eight inputs shown in Tables 2 and 3, and three output quantities of interest (QoI): power, axial thrust, and mass flow rate. Finally, we must also consider the convergence of the CFD simulation, as results exhibiting poor convergence cannot be considered. The initial DoE run was done using 20 sets of input parameters, allowing for a reasonable initial population of the space. Analysis of variance (ANOVA) on the DoE showed that the three outputs of interest were most sensitive to different inputs. Power was most affected by the shroud outlet angle, axial thrust was most affected by the hub outlet angle, and mass flow rate was about equally affected by the hub outlet angle and the shroud inlet angle. Globally, these latter two are the most influential parameters.

Assessment of the Model

Leave-one-out analysis is performed to assess the robustness of the surrogate model. A model generated with 19 samples should not be significantly different than one generated with all 20 samples, so the model is regenerated using all 19-element subsets, and the correlation of the reduced model can be computed against the full model. Globally, correlation coefficients were computed as follows:

Axial thrust	0.987
Mass flow	0.964
Power	0.669

Correlation coefficients above 0.6 indicate this model fits well with the data and is sufficiently well-resolved to serve as the foundation for automatic optimization.

Visualizing the DOE space is important to consider whether or not this optimization project is reasonable. After all, if we have chosen to vary parameters that have little or no effect on the outputs, then no amount of acceleration with the most sophisticated AI/ML kernels in existence will drive us to a useful result. However, it is impossible to draw a 12-dimensional plot. However, for any space, a mapping can be found to and from which we can produce contour plots and heat maps. Self-organizing maps are a way of using unsupervised machine learning to find such a mapping that ensures that sets of experiments with similar parameters are clustered together, with the inputs mapped to so that the topology of the space is visually intuitive. Note that the vertical and horizontal axes of a self-organizing map are meaningless. These maps simply allow us to qualitatively judge correlations.

In Figure 2, we see self-organizing maps for axial offset (AXIAL_OFFSET), power (Restart_U_POWER), and shroud exit angle (SHROUD_EXITANGLE). What we see is that the power and shroud exit angle are correlated, with high and low bands following approximately the same shape, while the axial offset bands are completely uncorrelated.

Figure 2: Self-organizing maps for axial offset, power, and shroud exit angle. Overlapping red zones indicate power and exit angle are strongly correlated

After verifying that the design space makes sense, optimization proceeds using the surrogate model and additional CFD runs. Each CFD run takes approximately 45 minutes, so the use of full CFD is minimized. First, inner optimization cycles are performed using the computationally cheap surrogate model, seeking optimal power while respecting design constraints. This results in a new candidate being identified. Then, CFD is executed on the candidate, and the surrogate model is updated. This process is executed until convergence is obtained. 22 sequential CFD runs were needed to fully optimize the design, a process which was completed in under 24 hours.

Figure 3: Optimization of power

Results, Summary, and Conclusions

The optimized design delivers nearly a 1% power improvement over the original design. Figure 4 shows that this improvement comes primarily via decreasing the zone of detached flow at the suction side of the rotor.

Figure 4: Contour plots of Mach number for the new design

Cadence Fidelity software was used to design and optimize a low-pressure steam turbine stage under strict design constraints. Fine Agile, Fine Turbo, and Fine Design3D were all used together to automatically optimize the design, achieving a nearly 1% power uplift over the previous design. Data analytics tools within the Fine Design3D environment, particularly self-organizing maps, proved capable of verifying that the design space was properly parameterized to find a useful optimum. Surrogate modeling combined with occasional CFD-based updates proved to be capable of generating an optimal solution in under 24 hours.

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